A rectangle ABCD, where A≡0,0, B≡4,0, C≡4,2, D≡0,2, undergoes the following transformation successively :i. f1x,y→y,xii. f2x,y→x+3y,yiii. f3x,y→x−y/2,(x+y/2)The final figure will be

Clearly, A will remains as 0,0; f1will make B as(0, 4) f2 will make it 12,4, and f3 will make it (4, 8) f1 will make C as 2,4,f2 will make it 14,4, and f3 will make it 5,9. Finally, f1 will make D as 2,0,f2will make it 2,0 and f3 will make it 1,1. So, we finally get A≡0,0, B≡4,8, C≡5,9 and D≡1,1. Hence,mAB=84, mBC=9−85−4=1, mCD=9−15−1=84mAD=1, mAC=95,mBD=8−14−1=73Hence, the final figure will be a parallelogram